There are some contradictions in the literature on the structure of micelles formed by the BRIJ-35 surfactant in water. One can find reasonable differences in the aggregation numbers and micellar sizes, but there is a lack of data on the intermicellar structure. In this study, we reevaluated the small-angle neutron scattering experiments performed previously on the BRIJ-35 surfactant in the concentration range of 5-200 g/dm3 at 20, 40, and 60 degrees C. The data were analyzed with a reverse Monte Carlo-type method developed recently for colloids. The micelles were modeled as spherical cores representing the hydrophobic parts and number of balls put on the cores to mimic the hydrated hydrophilic chains. The simulations provided data on the mean aggregation number and on the extent of hydration of the hydrophilic shell of the micelles. We obtained intermicellar pair-correlation functions indicating different micelle-micelle interactions from the usually assumed hard-sphere ones.